At age 24, Urgellés batted .362 in the 2005-2006 Serie Nacional, finishing sixth in batting average while playing on the championship team. In 2006 Haarlem Baseball Week, he dazzled, going 8 for 10 with two doubles, a triple, a walk, four runs and four RBI but Cuba finished second. He got his first starting duty in a major international event in the 2006 Intercontinental Cup and played very well, hitting .395/.410/.684 with 15 RBI in nine games. He tied eight others for second in home runs (2), one behind leader Brad Harman, led in RBI (four ahead of Young-seop Bae) and tied for third with 15 hits (even with Chien-Ming Chang and Sharnol Adriana, trailing Alexander Mayeta and Yung-Chi Chen). He was 1 for 5 with a triple and 3 RBI in the 6-3 Gold Medal game win over the Dutch national team. He won the award as the tourney's top defensive player (1.000 fielding percentage, one assist) and joined Cuban teammates Giorvis Duvergel and Cepeda on the tourney All-Star team. Urgellés wrapped up his honors with the tournament MVP award.

In the 2006-2007 Serie Nacional, Yoandry hit .351/~.447/.522 and led the way with 27 stolen bases. Through 2006-2007, his career line in Cuban league play was .339/~.424/.480.

Urgellés hit .316/.435/.316 in the 2007 Pan American Games to help Cuba win Gold. He scored four runs in five games, second to Duvergel on the champions. In the 2007 Baseball World Cup, Urgellés batted .294/.375/.647 with 8 runs and 11 RBI in 10 games. In the Gold Medal game, he went 1 for 4 with a run as Cuba lost 6-3 to the US, spoiling their bid for a 10th straight Cup title. Urgellés was not named to the tourney All-Star team as Cepeda, Colby Rasmus and Trent Oeltjen were the outfielders chosen.

Urgellés produced at a .374/.473/.689 clip in the 2007-2008 Serie Nacional. He tied Leslie Anderson for 5th in total bases (186), 6th in RBI (74), 4th in average, third in slugging behind Alexei Bell and Alfredo Despaigne, tied Yohenis Céspedes for 4th in runs (82) and tied for 7th in doubles (24). His 17 homers just missed the top 10. After leading in steals a season earlier, he only swiped 7 in 10 tries. Urgellés joined Bell and Despaigne on the Serie Nacional All-Star outfield.